A075269 Product of Lucas numbers and inverted Lucas numbers: a(n)=A000032(n)*A075193(n).

2, -3, 12, -28, 77, -198, 522, -1363, 3572, -9348, 24477, -64078, 167762, -439203, 1149852, -3010348, 7881197, -20633238, 54018522, -141422323, 370248452, -969323028, 2537720637, -6643838878, 17393796002, -45537549123, 119218851372, -312119004988, 817138163597

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Sep 11 2002

Keywords

• easy
• sign

Links

• Index entries for linear recurrences with constant coefficients, signature (-2,2,1).

Crossrefs

Cf. A000032, A002878, A075193.

Programs

Mathematica

CoefficientList[Series[(2 + x + 2x^2)/(1 + 2x - 2x^2 - x^3), {x, 0, 30}], x]
LinearRecurrence[{-2,2,1},{2,-3,12},30] (* Harvey P. Dale, Jun 30 2022 *)

PARI

a(n)=1+(-1)^n*(fibonacci(2*n)+fibonacci(2*n+2))

Formula

a(n) = 1 + (-1)^n*A002878(n).

From Michael Somos, Apr 07 2003: (Start)

G.f.: (2+x+2x^2)/((1+3x+x^2)(1-x)).

a(n) = -3a(n-1) - a(n-2)+5 = -2a(n-1) + 2a(n-2) + a(n-3) = a(-1-n). (End)

Sum_{n>=0} 1/a(n) = sqrt(5)/10. - Amiram Eldar, Jan 15 2022

a(n) = (-1)^n*A215602(n). - R. J. Mathar, Jul 09 2024

a(n) - a(n-1) = (-1)^n* A054888(n), n>0. - R. J. Mathar, Jul 09 2024